Nonlinear mixed ∗-Jordan n-derivations on ∗-algebras

Let [Formula: see text] be a ∗-algebra with unity [Formula: see text] and a nontrivial projection [Formula: see text]. In this paper, it is shown that if a map [Formula: see text] satisfies [Formula: see text] for all [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for all [Formula: see text], where [Formula: see text], then [Formula: see text] is an additive ∗-derivation. Moreover, we shall call such a map [Formula: see text], a nonlinear mixed ∗-Jordan [Formula: see text]-derivation. As applications, we will characterize nonlinear mixed ∗-Jordan [Formula: see text]-derivation in standard operator algebras and von Neumann algebras.